📚 Electric and Magnetic Fields | 电场与磁场
In A-Level Physics, electric and magnetic fields are fundamental to understanding forces, energy, and modern technology. This revision guide covers key concepts from Coulomb’s law to electromagnetic induction, providing detailed explanations and worked comparisons.
在 A-Level 物理中，电场与磁场是理解力、能量和现代科技的基础。本复习指南涵盖从库仑定律到电磁感应的关键概念，提供详细的解释和对比。
1. Coulomb’s Law and Electric Force | 库仑定律与电场力
Coulomb’s law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The force is attractive for opposite charges and repulsive for like charges.
库仑定律指出两点电荷之间的力与电荷量的乘积成正比，与它们之间的距离平方成反比。异种电荷相互吸引，同种电荷相互排斥。
F = k |Q₁Q₂| / r² with k = 1/(4πε₀)
where ε₀ is the permittivity of free space. The constant k ≈ 8.99 × 10⁹ N m² C⁻².
其中 ε₀ 是真空介电常数。常数 k ≈ 8.99 × 10⁹ N m² C⁻²。
2. Electric Field Strength | 电场强度
Electric field strength E at a point is defined as the force per unit positive charge experienced by a small test charge placed at that point. E = F / q. Its unit is N C⁻¹ or V m⁻¹.
电场强度 E 定义为单位正电荷在该点所受的力。E = F / q，单位是 N C⁻¹ 或 V m⁻¹。
For a point charge, the radial field strength is given by:
对于点电荷，径向电场强度公式为：
E = k Q / r²
Field lines point away from positive charges and toward negative charges. The field is strongest where lines are most dense.
电场线从正电荷出发，指向负电荷。电场强度最大的地方电场线最密。
3. Electric Potential and Potential Difference | 电势与电势差
Electric potential V at a point is the work done per unit positive charge to bring a test charge from infinity to that point without acceleration. V = W / q. The unit is the volt (V).
电势 V 是单位正电荷从无穷远处无加速地移动到该点所做的功。V = W / q，单位是伏特 (V)。
For a point charge, V = k Q / r. The potential is a scalar quantity and can be positive or negative.
对于点电荷，V = k Q / r。电势是标量，可为正或负。
Potential difference (p.d.) between two points drives current. Equipotential surfaces are perpendicular to field lines.
两点之间的电势差驱动电流。等势面与电场线垂直。
4. Capacitors and Energy Storage | 电容器与能量存储
A capacitor stores charge and energy. Capacitance C = Q / V, measured in farads (F). For a parallel-plate capacitor, C = ε₀εᵣ A / d, where εᵣ is the relative permittivity of the dielectric.
电容器存储电荷和能量。电容 C = Q / V，单位是法拉 (F)。平行板电容器的电容公式为 C = ε₀εᵣ A / d，εᵣ 是介质的相对介电常数。
The energy stored is E = ½ Q V = ½ C V² = ½ Q² / C. The discharge of a capacitor through a resistor follows an exponential decay.
储存的能量 E = ½ Q V = ½ C V² = ½ Q² / C。电容器通过电阻放电遵循指数衰减规律。
5. Moving Charges and Magnetic Fields | 运动电荷与磁场
A magnetic field is a region where a moving charge or a current-carrying conductor experiences a force. Magnetic field lines point from north to south outside a magnet. The field strength B (magnetic flux density) is measured in tesla (T).
磁场是运动电荷或通电导线受力的区域。磁感线在磁体外从北极指向南极。磁感应强度 B 的单位是特斯拉 (T)。
Current-carrying wires create circular magnetic fields (right-hand grip rule). Solenoids and electromagnets produce uniform fields inside.
通电导线产生环绕磁场（右手螺旋定则）。螺线管和电磁铁内部产生匀强磁场。
6. Magnetic Force on a Current-Carrying Conductor | 磁场对通电导线的作用力
A conductor of length L carrying current I in a magnetic field B experiences a force F = B I L sinθ, where θ is the angle between the conductor and the field. The maximum force occurs when the conductor is perpendicular to the field.
长度为 L 的通电导线在磁场 B 中受到力 F = B I L sinθ，其中 θ 是导线与磁场的夹角。当导线与磁场垂直时力最大。
The direction of the force is given by Fleming’s left-hand rule: thumb – force, forefinger – field, second finger – current (conventional).
力的方向由左手定则判断：拇指——力，食指——磁场，中指——电流（正电荷方向）。
7. Motion of Charged Particles in Magnetic Fields | 磁场中带电粒子的运动
A charged particle moving perpendicular to a uniform magnetic field undergoes circular motion. The centripetal force is provided by the magnetic force: F = B q v = m v² / r. Hence the radius r = m v / (B q).
带电粒子垂直进入匀强磁场时做圆周运动。向心力由磁力提供：F = B q v = m v² / r，因此轨道半径 r = m v / (B q)。
The period T = 2π m / (B q) is independent of speed, which is used in cyclotrons and mass spectrometers.
周期 T = 2π m / (B q) 与速度无关，这一特性用于回旋加速器和质谱仪。
8. Magnetic Flux and Flux Linkage | 磁通量与磁链
Magnetic flux Φ through an area A is defined as Φ = B A cosθ, where θ is the angle between the field and the normal to the area. Flux is measured in weber (Wb).
通过面积 A 的磁通量定义为 Φ = B A cosθ，θ 是磁场与面积法线的夹角。磁通量单位是韦伯 (Wb)。
Flux linkage NΦ for a coil of N turns is the product of number of turns and flux through each turn.
线圈的磁链 NΦ 等于匝数乘以每匝的磁通量。
When flux linkage changes, an e.m.f. is induced (Faraday’s law).
当磁链发生变化时，产生感应电动势（法拉第定律）。
9. Faraday’s Law and Lenz’s Law | 法拉第电磁感应定律与楞次定律
Faraday’s law: The magnitude of the induced e.m.f. is equal to the rate of change of magnetic flux linkage:
法拉第定律：感应电动势的大小等于磁链的变化率：
ε = – N ΔΦ / Δt
The negative sign represents Lenz’s law: the direction of the induced current opposes the change in flux that produced it. This is a consequence of conservation of energy.
负号代表楞次定律：感应电流的方向总是阻碍引起感应的磁通量变化。这是能量守恒的体现。
10. Comparing Electric and Magnetic Fields | 电场与磁场对比
| Electric Fields | Magnetic Fields |
| Act on stationary and moving charges | Act only on moving charges |
| Field lines start on positive charges, end on negative | Field lines are closed loops (no monopoles) |
| E = F/q (N C⁻¹), potential V = W/q | B = F/(I L) (T), force given by left-hand rule |
| Force parallel to field for charges | Force perpendicular to both v and B |
| Can store energy in capacitors | Energy stored in inductor magnetic field |
Both fields share similar mathematical forms: Coulomb’s law vs. magnetic force between currents, but the absence of magnetic monopoles creates fundamental differences.
两种场在数学形式上有相似之处：库仑定律与电流之间的磁力，但由于没有磁单极子而存在根本差异。
11. Applications and Exam Tips | 应用与备考技巧
Applications: Capacitors in timing circuits, defibrillators; electromagnets in relays, loudspeakers; motors and generators; particle accelerators and mass spectrometers; transformers for voltage change.
应用：电容器用于定时电路、除颤器；电磁铁用于继电器、扬声器；电动机和发电机；粒子加速器和质谱仪；变压器变换电压。
In Edexcel papers, common pitfalls include forgetting to square the distance in Coulomb’s law, misapplying the left-hand rule, confusing flux and flux linkage, and neglecting the negative sign in Lenz’s law. Always draw clear diagrams with field lines and indicate directions.
在 Edexcel 考试中，常见错误包括忘记库仑定律中的距离平方、错误使用左手定则、混淆磁通量与磁链、忽略楞次定律中的负号。建议画出示意图，标清方向。
Use dimensional analysis to check equations: e.g., B I L must give newtons. Practice calculations with energy in capacitors and circular motion of charges.
用量纲分析检查公式：例如 B I L 必须得出牛顿。加强电容器能量与电荷圆周运动的计算练习。
Published by TutorHao | Physics Revision Series | aleveler.com
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